Specific Examples
Calculating Mulitvariate Statistics using Stand-alone Functions
While the four MINOTAUR multivariate statistics can be calculated within the MINOTAUR GUI, users may sometimes wish to calculate them outside of the GUI. Users would normally load their own dataframe from an CSV/TSV or Rdata file. Here data will be created using the rnorm function.
# load MINOTAUR
library(MINOTAUR)
# set the number of observations (e.g., loci)
observations <- 1000
# set arbitrary observation IDs using seq
# (to mimic positional metadata normally found in genome-wide data)
obsID <- seq(1, observations, by=1)
# generate distributions using rnorm for 5 variables (e.g., statistics)
var1 <- rnorm(observations)
var2 <- rnorm(observations)
var3 <- rnorm(observations)
var4 <- rnorm(observations)
var5 <- rnorm(observations)
# bind variables into a data frame
allVar <- cbind(obsID, var1, var2, var3, var4, var5)
# set the columns to use for multivariate inference
columns <- 2:6
# run each multivariate function
# note that these functions cannot accommodate any missing data
# Mahalanobis
Md <- Mahalanobis(allVar, columns)
# Harmonic mean distnace
Hd <- harmonicDist(allVar, columns)
# Nearest neighbor distance
Nd <- neighborDist(allVar, columns)
# Kernel density
# first determine the optimal bandwidth based on the data
# create a range of bandwidths
bw <- c(seq(0.01,0.1,by=0.01),seq(0.2,1,by=0.1))
# determine the optimal bandwidth
Kd.ML <- kernelDeviance(allVar, columns, bandwidth=bw)
bw.best <- bw[which(Kd.ML==max(Kd.ML))[1]]
# calculate the kernel density
Kd <- kernelDist(allVar, columns, bandwidth=bw.best)
# plot a histogram of the multivariate statistics
hist(Md, bins=100, xlab="Mahalanobis distance", main="Histogram of Mahalanobis distance")
hist(Hd, bins=100, xlab="Harmonic mean distance", main="Histogram of Harmonic mean distance")
hist(Nd, bins=100, xlab="Nearest neighbor distance", main="Histogram of Nearest neighbor distance")
hist(Kd, bins=100, xlab="Kernel density", main="Histogram of Kernel density")
# users can identify outliers using these distributionsCalculating and Visualizing Multivariate Distributions using the MINOTAUR GUI
Initiating the MINOTAUR GUI
The above workflow can also be performed within the MINOTAUR GUI, which provides much richer visualization of multivariate distance distributions and outliers. To initiate the MINOTAUR GUI, type the following commands into R.
library('MINOTAUR')
MINOTAUR()The MINOTAUR GUI will then open in your default internet browser. This may take a minute, since dependencies need to be checked and possibly installed.
Overview
The Welcome page will greet you and includes a brief overview on the package and some basic navigation instructions.
Along the left-hand side of the window is a series of tabs allowing the user to move through the MINOTAUR menus. The Data tab is used to load and format data. The Outlier Detection tab is used to calculate multivariate measures using the data. Finally, the Produce Plots tab provides a series of useful plots for visualizing both univariate and multivariate distributions and outliers. Throughout this example, these menus will appear in bold and any submenus will appear in italics.
Inputing and Filtering Data
To get started, data must first be leaded into the GUI. Clicking on Data and Input Data will take the user to a menu for this. Users can select between using example data or uploading their own data from text files or an Rdata object. For this example, we will be using the ‘Human GWAS’ example dataset, which is simulated data that mimics what would be produced during a GWAS study (much like the simulated data we generated above).
When any dataset is selected or uploaded, the number of rows and columns will be reported to the right, above an interactive raw data table or a summary table.
Before proceeding to outlier detection, we will first do some data formatting in the Format Data submenu. This allows the user to first set position (i.e., bp) and grouping (i.e., chromosome) variables, which is useful for later plotting. For this dataset, the position variable is ‘BP’ and the grouping variable is ‘Chr’.
Users can also subset data a number of ways. First, one can decide which data variables (columns) to carry forward in the GUI by unselecting the ‘Use all remaining variables’ checkbox. The user can add variables and decide whether to retain or remove them from the dataset. Users also have the option of removing missing data in the form of ‘NA’, ‘NaN’, and ‘+/-Inf’. Missing data is prohibited in any MINOTAUR multivariate functions, so care should be taken to use these options and any other means to eliminate missing data. In this example, we will keep only the beta-distributed trait measurements (‘TraitN_Beta’) and will remove any forms of missing data (check all boxes).
To the right, some useful information is displayed. Along the top is a plot of the breakdown of data across grouping variables (e.g., the number of SNPs on each chromosome). Along the bottom is a view of the final data table with variables and missing data excluded.
Calculating Multivariate Measurements
The next major step in the MINOTAUR workflow is to calculate multivariate composite measures. By clicking on Outlier Detection and Find Outliers the user is brought to a series of menus to do this. Along the left side is a tabbed menu for generating and summarizing any multivariate measures. The summary table will appear blank at first, and multivariate measures can be added using either the ‘Distance-Based’ or ‘Density-Based’ tabs, which reflect the general manner multivariate measurements are made.
Under the ‘Distance-Based’ tab, the user has the ability to use the Mahalanobis, Harmonic Mean, and Nearest Neighbor distances. For each, the user should select the three retained variables (‘TraitN_Beta’) and the desired distance measurement. Upon clicking the ‘Calculate!’ button, the distance measure is calculated and a histogram of the measure across all loci is displayed to the right. Below, users can input a name for the measure, which becomes the variable name for the data generated, and a brief description. The user should, one at a time, calculate distance based measures for all three distances using the three traits and appropriate names and descriptions.
The same general options also appear under the ‘Density-Based’ tab, which is used to generate Kernel Density measurements. The user must also select a the ‘Bandwidth estimation method’ used to calculate the kernel size. Options include using an appropriate bandwidth for the data based on Silverman’s rule (default), setting a custom bandwidth, and using maximum likelihood to determine the optimal bandwidth to use (much more time consuming). For this dataset the maximum likelihood estimate of the best bandwidth is 0.01, so we will set a custom bandwidth with that value.
Between each, the user will notice that the summary table reporting multivariate measures will be populated. Users can use the menu near the bottom of the ‘Summary’ tab to both replot histograms and delete any generated multivariate measurements.
Visualizing Multivariate Distributions & Outliers
Finally, now that multivariate measures have been calculated, the user can proceed to generating plots and visually exploring the data (NOTE: the user can also visualize their data BEFORE outlier calculation. It is not necessary to calculate outliers first.). The submenus beneath Produce Plots include the plot type available in MINOTAUR. To demonstrate the general options available to the user when plotting, we will create a Manhattan plot of our multivariate measures using the Linear Manhattan Plot submenu.
Each plotting submenu contains two options menus and the resulting plot. The ‘Select Variables’ menu is used to manipulate what data are being plotted on each axis, plus intuitive, general attributes about the axes themselves. Under ‘Select y-axis’ we will select the output of our Nearest Neighbor Distance calculation (called ‘Nd’) to display a Manhattan plot of this distance across all loci in the dataset.
The ‘Select outlier variable’ gives us the ability to color points based on their position in the variable distribution (i.e., color outliers). In this circumstance, it makes the most sense to color the highest (upper) 1% tail of the Nearest Neighbor Distance, which represents those loci whose multivariate nearest neighbor distance distance is the greatest.
The ‘Adjust Plot Aesthetics’ menu provides numerous, intutive aesthetic options for the resulting plot. Here is a menu configuration that provides an intuitive Manhattan plot with outliers indicated by red dots.
And here is the resulting plot based on these options.
Part of the beauty of the MINOTAUR GUI is that multiple, stacked plots can be made, and when the plotting menus are collapsed, it provides the user with the ability to visually compare how various univariate and multivariate measures performed with the data, resulting in a figure like the following.
Users will see these general plotting options on the other plotting submenus and can use them to generate an array of plots that are useful for exploring their data.